On a Group Functor Describing Invariants of Algebraic Surfaces

Heiko Dietrich, Primoz Moravec

Research output: Contribution to journalArticleResearch

Abstract

Liedtke (2008) has introduced group functors K and K~, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of central extensions and Schur multipliers. In this work we relate K and K~ to a group functor τ arising in the construction of the non-abelian exterior square of a group. In contrast to K~, there exist efficient algorithms for constructing τ, especially for polycyclic groups. Supported by computations with the computer algebra system GAP, we investigate when K(G,3) is a quotient of τ(G), and when τ(G) and K~(G,3) are isomorphic.
Original languageEnglish
Article numberOWP-2019-08
Number of pages15
JournalOberwolfach Preprints (OWP)
Volume2019
DOIs
Publication statusPublished - 1 Mar 2019

Cite this

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abstract = "Liedtke (2008) has introduced group functors K and K~, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of central extensions and Schur multipliers. In this work we relate K and K~ to a group functor τ arising in the construction of the non-abelian exterior square of a group. In contrast to K~, there exist efficient algorithms for constructing τ, especially for polycyclic groups. Supported by computations with the computer algebra system GAP, we investigate when K(G,3) is a quotient of τ(G), and when τ(G) and K~(G,3) are isomorphic.",
author = "Heiko Dietrich and Primoz Moravec",
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On a Group Functor Describing Invariants of Algebraic Surfaces. / Dietrich, Heiko; Moravec, Primoz.

In: Oberwolfach Preprints (OWP), Vol. 2019, OWP-2019-08, 01.03.2019.

Research output: Contribution to journalArticleResearch

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AU - Moravec, Primoz

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AB - Liedtke (2008) has introduced group functors K and K~, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of central extensions and Schur multipliers. In this work we relate K and K~ to a group functor τ arising in the construction of the non-abelian exterior square of a group. In contrast to K~, there exist efficient algorithms for constructing τ, especially for polycyclic groups. Supported by computations with the computer algebra system GAP, we investigate when K(G,3) is a quotient of τ(G), and when τ(G) and K~(G,3) are isomorphic.

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DO - 10.14760/OWP-2019-08

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JO - Oberwolfach Preprints (OWP)

JF - Oberwolfach Preprints (OWP)

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